NDT Solution
Shear Wave Polarization Follows Twist of
Rectangular Steel Bar
by James
C. Hurd,* Toan H. Nguyen+ and Lawrence
C. Lynnworth±
This month's featured article examines the propagation of shear waves in a twisted steel bar. The authors have concisely outlined the salient findings of their study and provided a clear distinction of their research from earlier investigations. Results from this study could have many practical applications.
G.P Singh
Associate Technical Editor
INTRODUCTION
The question of ultrasonic shear wave polarization arises when manufacturing a shear wave transducer, when analyzing mode conversion, in studies of stress (Shahbender, 1961; Crecraft, 1967), in testing welds by the tandem method (Lovelace, 1980), in testing composites for ply orientation (Hsu et al., 2002; Fei and Hsu, 2002) and in various research studies (Einspruch, 1964). (Readers interested in comparing the present work's ultrasonic shear wave polarization measurement and interpretation with optical polarization analyzers are referred to Jaroszewicz and Marc [2003]. An example of shear wave polarization applied to seismology/geophysics is provided by Zeng and MacBeth [1993]).Figure 1 - Shear wave polarization experiment conducted by Lynworth (1967) on a steel bar measuring 13 by 13 by 305 mm (0.5 by 0.5 by 12 in.)
It has been known for some time that the speed of shear waves in elastic solids depends on stress (Bridgeman, 1927) and on the polarization being parallel or perpendicular to the stress (Shahbender, 1961). Lynnworth (1967) reported that if shear waves propagate along the long axis of a twisted steel bar of square cross section, strained beyond the elastic limit, the shear waves tend to follow the twist (Figure 1). That remark was a minor part of a paper dealing with shear wave coupling and applications and the polarization in a twist deformed bar did not receive much attention. For example, no attempt was made in that paper to sort out whether the rotation was due to the crystal lattice being twisted, the boundary acting like a waveguide or some combination of the two. The present study is an attempt to sort out the relative contributions and to quantify the earlier observation that the polarization tends to follow the twist.
The angle for maximum signal turned out to equal the angle of twist.
EXPERIMENTAL PROCEDURE
The experimental procedure is explained with the aid of Table 1 and Figure 2. The UNS G10180 carbon steel (ASTM A108-99) bars that were used in the tests reported here, seven total, are shown in Figure 2a prior to twisting.Figure 2 - Photo of seven steel bars: (a) straight before twisting; (b) six twisted and one straigh; (c) midsection turned down for the 30, 60, 90 degree bars.
The seven were prepared from two similar 1.8 m (6 ft) bars by sawing specimens to equal lengths of approximately 300 mm (11.8 in.) with ends subsequently milled flat and perpendicular to the axes. Cross sectional dimensions were 19 by 22 mm (0.75 by 0.88 in.), which is a commercially available standard rectangular shape. Prior to twisting, shear waves transmitted along their lengths revealed no rotation of polarization.
The shear wave transducers used in these tests are commercially available types, nominally 2.25 MHz. They were coupled using a high viscosity couplant. Alignment, thumbscrew pressure and graduated angle scale were provided by the slotted clamp shown in Figure 3a. The electronic measuring system is basically a pulser/receiver and display. Amplitudes were recorded after the thumbscrew was finger tightened against the shear wave contact transducer. ScanView software allows one to acquire waveforms and play back the experiment as a function of transducer polarization angle. A little rotation of one transducer relative to the other, (±5 degrees) produces little change to the received amplitude A. Large rotation, however, yields a received signal amplitude that approximately follows - that is, resembles - the cosine function (Figures 3b and 3c).
Figure 3 - Shear wave transducers: (a) in a block diagram; (b) oscillograms at 45 degree intervals - 0 to 180 degrees show that, for an untwisted bar, if the receiving transducer is rotated relative to the transmitting transducer, the received signal magnitude and polarity approximately follows a cosine functions; (c) expanded view of 0 and 180 degree oscillograms shows polarity difference corresponding to transducer parallel versus antiparallel. (Both traces have been multiplied by -1 to compensate for negative spike excitation). Orthogonal transducer yield a small but nonzero amplitude: the expected null is imperfect. The parallel and antiparallel traces in 3c also shows that the period of the first large received cycle is just under 1 µs. this means the corresponding frequency is just over 1 MHz, but not 2.25 MHz. Their spectra in fact pear near 1.1 MHz.
At 2.25 MHz, the shear wavelength
. A spectral test of the received signal, however, showed that the frequency of maximum intensity was 1.1 MHz, for which
. This means the bars were slightly under ten wavelengths in cross section, depending partly on where along the bar the wavelength would be measured. That is, if the spectrum shifts down from 2.25 MHz to 1.1 MHz as the wave propagates, the wavelength corresponding to the peak frequency in the spectrum increases from transmitting to receiving transducer.
Next, specimens 2 through 7, all coming from one bar, were twisted at room temperature beyond their elastic limit and permanently deformed to angles of 15, 30, 45, 60, 75 and 90 degrees, as shown in Figure 2b. They were not annealed afterwards. The twist is confined to the middle 150 mm (5.9 in.) portion. The receiving transducer was then rotated in 5 degree increments. At each angle, the amplitude and phase of the received shear wave was recorded by storing the complete waveform. In this way, we determined for each twist receiver angles for maximum amplitude, relative to the launching transducer's polarization (Figure 4). The angle for maximum signal turned out to equal the angle of twist.
Figure 4 - Shear wave polarization experiments on twisted bars: the angle between transducers compensates for a 5 degree bias.
After determining that the polarization followed the twists shown in Figure 2b, three twists were machined away, so that all visual indication of 30, 60 and 90 degree twists was removed except for the rectangular end portions. The rectangular end portions were retained for about 25 mm (1 in.) at each end to accommodate the clamp of Figure 3a. The obvious angle between these end sections preserved a permanent unambiguous record of each specimen's twisted history. The amplitude versus angle experiment was repeated for these three bars after the waveguiding contribution had been machined away from the midsection. Results are summarized by the lower three points in Figure 4. The polarization no longer follows the twist.
DISCUSSION OF RESULTS
In contrast to earlier work such as Bridgeman (1927), Shahbender (1961) or Crecraft (1967), in which the effect of stress on shear wave velocity was studied, including shear wave polarization parallel or perpendicular to the stress, the present work deals with strains in permanently deformed bars. As in Lynnworth (1967), the present measurements concentrate on amplitude measurements as a function of angle, not transit time. Another difference is that the velocity effects reported for example by Shahbender (1961) or Crecraft (1967) can be measured using pulse echo, while the amplitude effect due to polarization rotating presumably is cancelled on pulse echo because whatever rotation occurs on the first traverse is undone on the return path. Amplitudes versus angle were measured for Figure 4 using through transmission. The results summarized in Figure 4 are that polarization follows the twisted rectilinear waveguide to at least 90 degrees. But polarization does not follow the twist for a cylindrical bar (circular cross section). In other words, the twisted crystal lattice does not appear to influence polarization. These remarks are based on an experimental procedure having a limit of angular resolution of ±5 degrees.Another way to summarize the present results is to say the ultrasonic shear wave polarization in a rectangular solid elastic waveguide appears to behave analogously to the transverse electric field in a rectangular microwave hollow waveguide, with respect to polarization. Twists in hollow microwave waveguides, according to Reich et al. (1957) are used to orient the guide to conform to other devices to which it is coupled (for example, an oscillator), to obtain a sought plane of polarization for waves exiting the guide or to change direction.
CONCLUSIONS
Unannealed, initially straight rectangular steel bars were twisted along the middle 150 mm (5.9 in.) of their 300 mm (11.8 in.) length. It appears that for twists up to 90 degrees, when transverse shear waves propagate along the long axis of the bar, the polarization follows the twist to within ±5 degrees. But if the twisted portion is turned down to a circular cross section, polarization no longer follows the twist. The twisted crystal lattice does not appear to influence polarization, at least not within the ±5 degrees angular resolution limits of the present experiments.Following the twist, therefore, is attributed to the waveguiding effect of the helical rectilinear boundary.
These effects were observed at room temperature on through transmission by measuring the received amplitude versus angle between nominally 2.25 MHz transverse shear transducers. The specimens were UNS G10180 carbon steel, approximately 19 by 22 mm (0.75 by 0.88 in.) in cross section.
ACKNOWLEDGMENTS
The authors acknowledge helpful discussions with colleagues Agostino Abbate, Fred Hotchkiss, Tom Nelligan, Ken Fowler, David R. O'Connor and Bob Gilmore. The bars were twisted at Artisan Industries, Inc., coordinated by Ralph Bailey. The clamps were made by Carl Padovano of C&A Machine Company, both companies located in Waltham, Massachusetts. The authors acknowledge GE Panametrics's support and permission to release substantial portions of its copyrighted report UR-266.
REFERENCES
ASTM International, ASTM A108-99, Standard Specification for Steel Bars, Carbon, Cold-finished, Standard Quality, West Conshohocken, Pennsylvania, ASTM, 1999.Bridgeman, P.W., "Compressibility and Pressure Coefficient of Resistance of Ten Elements," American Academy of Arts and Sciences, Vol. 62, 1927, pp. 207-226.
Crecraft, D.I., "The Measurement of Applied and Residual Stresses in Metals Using Ultrasonic Waves," Journal of Sound and Vibration, Vol. 5, No. 1, 1967, pp. 173-192.
Einspruch, N.G., "Generation of Circularly Polarized Transverse Shear Waves," Journal of the Acoustical Society of America, Vol. 36, No 5, 1964, pp. 971-972.
Fei, D. and D.K. Hsu, "A Model and Experimental Study of Fiber Orientation Effects on Shear Wave Propagation through Composite Laminates," Journal of the Acoustical Society of America, Vol. 111, No. 2, 2002, pp. 840-855.
Hsu, D.K., D. Fei and Z. Liu, "Ultrasonically Mapping the Ply Layup of Composite Laminates," Materials Evaluation, Vol. 60, 2002, pp. 1099-1106.
Jaroszewicz, L.R. and P. Marc, "Inline Fiber-optic Polarization Analyzers for Sensor Application," IEEE Sensors Journal, Vol. 3, No. 1, 2003, pp. 71-79.
Lovelace, J., "Polarization Effects in Shear Wave Testing," Materials Evaluation, Vol. 38, No. 12, 1980, pp. 61-67.
Lynnworth, L.C., "Ultrasonic Probes Using Shear Wave Crystals, Part 1, Principles," Materials Evaluation, Vol. 25, No. 12, 1967, pp. 265-277.
Reich, J.R., J.G. Skalnik, P.F. Ordung and H.L. Krauss, Microwave Principles, New Jersey, D. Van Nostrand, 1957.
Shahbender, R.A., "Nondestructive Measurement of Tensile and Compressive Stresses," IRE Transactions on Ultrasonic Engineering, Vol. 8, No. 2, 1961, pp. 19-22.
Zeng, X. and C. MacBeth, "Accuracy of Shear-wave Polarization Estimates from Near-offset VSP Data," Canadian Journal of Exploration Geophysics, Vol. 29, No. 1, 1993, pp. 246-265.
* GE Panametrics, 221 Crescent St., Waltham, MA 02453; (781) 472-1608; fax (781) 894-5785; e-mail <james.hurd@ps.ge.com>.
+ GE Panametrics, 221 Crescent St., Waltham, MA 02453.
± Lynnworth Engineering, 77 Graymore Rd., Waltham, MA 02451-2201; (781) 894-2309; e-mail <larry@kynosoura.com>.
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